Micromechanics models for non-linear behavior of piezo-electric fiber reinforced composite materials

Surface stress and agglomeration effects on nonlocal biaxial buckling polymeric nanocomposite plate reinforced by CNT using various approaches

“…One of these averaging methods is representative volume element. Linear effective elastic for polymeric nanocomposite rectangular plate in the micromechanical approach can be written as [26]:…”

Model for piezoelectric/ferroelectric composites polarized with interdigitated electrodes

“…Other models were proposed for the analysis of history dependent non-linear effects in piezoelectric composite materials. The model proposed by Tan and Tong [26] uses uniform field model to capture the response to moderate and monotonic electric fields. Aboudi [27,28] uses a homogenization micro-mechanic based model for the study of the hysteretic response of a composite reinforced with ferroelectric fiber with periodic structure.…”

“…Having this objective in mind, based on Luccioni [30] original work and extending it to include electromechanical coupling, an alternative way of expressing the constitutive equation of each constituent is proposed in this paper. Using this approach, the composite behavior can be obtained in a relative simple manner introducing hypothesis similar to those of the classic mixture theory [26]. Regarding each field variable, strain, electric field, mechanical stress and electric displacement the material could work in series or parallel, depending on the relative disposition of each phase.…”

An incremental algorithm for static shape control of smart structures with nonlinear piezoelectric actuators

“…where eðEÞ 2 R 3Â6 is the piezoelectric stress coefficient matrix, whose entries can be expressed as functions of the applied electric field density for nonlinear piezoelectric materials (Crawley and Lazarus, 1991;Tan and Tong, 2001). In general, each entry of the piezoelectric stress coefficient matrix can be approximated by the first several terms of its Taylor expansion.…”